A223091 Numbers k such that sigma(k - 2) = sigma(k + 2).

53, 68, 117, 222, 321, 1005, 2587, 4026, 4185, 4197, 5722, 5828, 5961, 8006, 8376, 11661, 12369, 12563, 13583, 14340, 15367, 16118, 17842, 18720, 20543, 25132, 29395, 30172, 32667, 36518, 39915, 40662, 42425, 42924, 47843, 49764, 50040, 50437, 52314, 53220

Offset: 1

Author

Irina Gerasimova, Mar 22 2013

Keywords

• nonn

Comments

Corresponding values of sigma(n - 2) = sigma(n + 2): 72, 144, 144, 504, 360, 1080, 3456, 7560, 4320, 5040, 15120, 11664, .... The first two values not divisible by 72 are for n = 21 and 23, a(n) = 15367 and 17842, sigma = 21120 and 41664. A search up to a(n) = 10^8 did not turn up any sigma not divisible by 24. - Michael B. Porter, Mar 28 2013

Examples

			sigma(53 - 2) = sigma(53 + 2) = 72, sigma(68 - 2) = sigma(68 + 2) = 144, sigma(117 - 2) = sigma(117 + 2) = 144, sigma(222 - 2) = sigma(222 + 2) = 504, sigma(321 - 2) = sigma(321 + 2) = 360.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A067135, A175876.

Programs

Mathematica

Select[Range[10000], DivisorSigma[1, # - 2] == DivisorSigma[1, # + 2] &] (* Alonso del Arte, Mar 23 2013 *)
Flatten[Position[Partition[DivisorSigma[1,Range[55000]],5,1],?(#[[1]] == #[[5]]&),{1},Heads->False]]+2 (* _Harvey P. Dale, Sep 14 2016 *)

PARI

is(n)=sigma(n-2)==sigma(n+2) \\ Charles R Greathouse IV, Mar 17 2014